Track-Before-Detect for an Active Towed Array Sonar

Transcription

1 17-20 Noveber 2013, Victor Harbor, Australia Track-Before-Detect for an Active Towed Array Sonar Han X. Vu (1,2), Sauel J. Davey (1,2), Fiona K. Fletcher (1), Sanjeev Arulapala (1,2), Richard Elle (1) and Cheng-Chew Li (2) (1) Defence Science and Technology Organisation, AUSTRALIA (2) School of Electrical and Electronic Engineering, University of Adelaide, AUSTRALIA ABSTRACT Conventional active sonar processing systes typically reduce the sensor data fro an intensity ap to a pointeasureent for via a detection thresholding process. This approach is often sufficient for detecting and tracking high signal-to-noise-ratio (SNR) targets but becoes ore challenging for low SNR targets. Track-Before-Detect (TkBD) is an alternative tracking technique that supplies raw sensor data to the tracker to deterine the presence and kineatic state of a target. This paper considers the application of TkBD to an active sonar tracking proble using the Histogra-Probabilistic Multi-Hypothesis Tracking (H-PMHT) algorith. To aid in the detection of targets in the sensor iage, the easureent odel for the standard H-PMHT algorith is extended to incorporate a bearingdependent point spread function. Using real data gathered fro sonar trials, the perforance of the resulting ultitarget TkBD algorith is shown to be ore robust at low SNR levels when copared against a conventional point easureent tracker based on Integrated Probabilistic Data Association. 1 INTRODUCTION The detection and tracking of low signal-to-noise-ratio (SNR) targets using an active towed array sonar is a non-trivial proble due to the coplex nature of the underwater acoustic environent. Active sonar detection and tracking is particularly challenging in littoral environents where perforance can be degraded by high levels of acoustic clutter that result in false alars, fluctuating target returns due to coplex tie-varying acoustic conditions, and a relatively low sonar data update rate. Traditionally, a sonar syste's detection and tracking capabilities have been considered separate functions. Conventional active sonar processing systes use beaforing and atched filter correlation with a replica of the transitted pulse to generate a sensor iage of the reflected acoustic intensity as a function of range and bearing. Typically, this sensor iage is noralised to reove ean background variations and a fixed threshold is applied to produce detections that are then provided to the tracker. The role of the tracker is to associate point-easureents fro a coon target across tie and return estiates of the target's trajectory. This approach is often sufficient for detecting and tracking high SNR targets but becoes ore challenging for low SNR targets, as the process of reducing the sensor iage to thresholded detections discards valuable target inforation. An exaple of active sonar tracking using conventional nonlinear Kalan filtering techniques on siulated easureents is provided by [2]. A coparison of a nuber of conventional ulti-target point-easureent trackers based on Global Nearest Neighbour and Probabilistic Data Association (PDA) using a siulated active sonar environent was addressed in [14]. Techniques based on the inclusion of target and clutter aplitude inforation within conventional pointeasureent trackers to iprove tracking perforance for active sonar have also been considered [1, 10]. The desire for ore robust trackers against low SNR targets in clutter-rich environents has resulted in the developent of alternative techniques that perfor concurrent detection and tracking, coonly referred to as Track-Before-Detect (TkBD). TkBD algoriths eliinate the thresholding process and directly use the sensor intensity data to deterine the presence and kineatic state of a target. A review of early TkBD algoriths for applications in iage sequences, radar and sonar is provided by [18]. These techniques have the potential to provide significant gains for both detecting and tracking low SNR targets in high clutter scenarios [8]. The first applications of TkBD to active sonar were based on dynaic prograing techniques, which use a fixed grid to odel the propagation of target states with tie [4, 9, 18]. Furtherore, ost of these techniques have been deonstrated with siulated data and the application of TkBD to real sea trials data has been liited [15]. This paper considers the application of an alternative TkBD technique called Histogra-Probabilistic Multiple Hypothesis Tracking (H-PMHT) [11, 16] to an active sonar tracking proble. In addition, the standard H-PMHT algorith is extended to incorporate a bearing-dependent point spread function. The perforance of the H-PMHT is copared with a conventional point-easureent tracker based on Integrated Probabilistic Data Association (IPDA) [6, 12]. The benefits of TkBD over conventional tracking is analysed in two representative acoustic environents using trials data fro an active towed array sonar syste. The paper is arranged as follows. Section 2 outlines the tracking proble for both the conventional and TkBD case. Section 3 gives a brief review of the IPDA approach to conventional tracking as well as an introduction to the H-PMHT algorith and its odification to incorporate a bearingdependent point spread function. A coparative study of the two algoriths is presented in Section 4 using real data gathered fro an active towed array sonar syste. Section 5 suarises and discusses avenues for future work. Australian Acoustical Society 1

2 17-20 Noveber 2013, Victor Harbor, Australia 2 ACTIVE SONAR PROBLEM In target tracking, the ain objective is to identify the nuber of targets and estiate their trajectories over tie using a sequence of noisy easureents. In practice, it is coon to assue stochastic odels for the syste target dynaics and sensor data. Define the state vector x t, which evolves with tie t Є N, where N is the set of all natural nubers. For conventional active sonar target tracking, it is sufficient to describe the target state using position and velocity in two-diensions. However in the TkBD case, it is coon to suppleent the state vector with the target aplitude, x t [ ] T x x& y y& =, (1) t t t t where = 1,, M denotes the target index in the case of a ultiple target scenario and M denotes the total nuber of targets. Generally, when analysing a dynaic syste, two odels are required; the target and easureent odels. The target odel describes the target state evolution with tie and can be expressed in ters of a linear discrete-tie stochastic odel = x t F t 1 x t 1 + v t 1, (2) where F t-1 is a known atrix describing a linear state transition fro x t-1 to x t, and v t-1 is an independent identically distributed (i.i.d.) syste noise sequence representing uncertainties in the target otion. For the active sonar tracking proble, the target odel needs to capture the dynaics of an underwater target. In this paper, it is assued that a nearly-constant-velocity odel is sufficient. The second odel required is the easureent odel, which relates the noisy easureents to the state x t. In conventional sonar tracking, it is assued that point-easureents are received in range and bearing, and are given by ζ t = ηt ( x t ) + µ t, (3) where µ t is an i.i.d. easureent noise sequence and η(x t ) denotes the easureent odel that aps the state into the easureent space. The set of received easureents which satisfy the threshold crossing requireents ay originate fro either clutter or target coponents and it is not guaranteed that returns fro each target will satisfy the threshold. In the TkBD case, the easureent odel relates iages z t in range and bearing to the target state x t. Let z t i denote the ith pixel in the easureent iage at tie t, and let z t = {z t i } i=1, I represent a stacked vector of all the pixels in the iage, where i is the pixel index and I is the total nuber of pixels in the easureent iage. For ease of presentation, we have used a stacked vector to represent the iage to allow single index referencing. A two diensional representation could just as easily have been used. We assue a pointscatterer target, such that the target contribution to the easureent iage can be described purely in ters of the point spread function (psf), h (x t ) z t M = = 1 A t h( x t ) + w t, (4) where w t is an i.i.d. easureent noise sequence. Note that the psf is a property of the sensor and is the sae for all targets, but can vary with different sensors. Assuing independent pixel noise, the likelihood for the iage z t can be factorised as p( z t x t I i ) = p( z x ). (5) t t i = 1 For active sonar tracking, the easureent process only observes the position coponent of the target, thus the easureent odel assues that the likelihood is independent of the target velocity coponent. To prevent nuerical probles, the log of the likelihood is also calculated. Under linear Gaussian assuptions, the optial finite diensional solution to the discrete-tie recursive Bayesian state estiation proble is the Kalan Filter (KF). However as the sensor iage is a function of range and bearing, approxiations or suboptial solutions ust be considered to accoodate the resulting non-linear easureent odel. Furtherore, the TkBD easureent odel defined by (4) is clearly a highly non-linear function of the target state. Thus only non-linear tracking ethods can be considered when using TkBD techniques. In the next section, a brief review of the IPDA approach for conventional tracking and the H- PMHT approach for TkBD will be given. 3 TRACKING ALGORITHMS 3.1 Integrated Probabilistic Data Association (IPDA) for Conventional Tracking One of the ain difficulties in point-easureent tracking is deterining which easureents arise due to a particular target and which easureents are the result of false alars or due to objects that are not of interest. This proble is referred to as data association. Under a particular data association hypothesis, the target state can be estiated using a KF or non-linear counterpart. Probabilistic Data Association (PDA) expresses the target state probability density function (pdf) as a su over data association hypotheses and provides expressions to deterine the probabilities of these hypotheses [6]. The resulting pdf is a Gaussian ixture, which is then approxiated by a single Gaussian. The Integrated PDA (IPDA) extends the target state-space by defining a binary existence variable that indicates whether or not there is actually a target present and assues that this variable evolves according to a Markov Chain. The IPDA provides equations for recursively updating the target states and the probability of target existence based on the PDA approach for data association [12]. The probability of existence can then be used to autoate track anageent. The advantages of IPDA are that it is coputationally inexpensive and can be ipleented as a odified KF: the target description consists only of a ean vector, a covariance atrix and a scalar existence probability. However, the algorith uses a single Gaussian coponent to approxiate the Gaussian ixture arising fro the su of data association hypotheses. This approxiation can be poor, especially when the ixture has ore than one doinant coponent. IPDA also assues the existence of at ost one target. 2 Australian Acoustical Society

3 17-20 Noveber 2013, Victor Harbor, Australia Figure 1. Bea pattern vs. bearing for transissions at broadside, near aft and aft of the array. In this paper, a single target IPDA tracker based on [12] is ipleented. However, a ulti-target track anageent logic is iposed based on the assuption that targets in the iage do not overlap or interact with each other. Joint Integrated Probabilistic Data Association (JIPDA) can be used for scenarios featuring interacting targets but it is ore coputationally expensive than IPDA [13] and is not considered here. Tracks are initiated when the estiated probability of track existence rises above a certain threshold. Likewise, track terination occurs when the probability of track existence falls below another threshold. 3.2 H-PMHT for TkBD The H-PMHT algorith is an efficient ulti-target approach to the TkBD proble. The technique is based on the generation of a synthetic histogra by quantising the energy in the sensor data followed by the application of Expectation- Maxiisation (EM) ixture odelling to describe the underlying data sources. The algorith nae stes fro the interpretation of the quantised data as a histogra and the use of the Probabilistic Multi-Hypothesis Tracking (PMHT) algorith [17] to perfor the association of the resultant easureent counts to target objects. In the final step of the derivation, the liit of the quantisation is taken and the original sensor data is recovered. Unlike other TkBD approaches, the H-PMHT algorith eploys a paraetric fitting approach and has been shown to give perforance that is close to the optial Bayesian filter at a fraction of the coputational cost [8]. The H-PMHT can be naturally extended to track in a ulti-target scenario but still has linear coplexity with the nuber of targets. The H- PMHT can also be applied to a wide range of probles as long as an appropriate state estiator exists to perfor the EM step of the algorith. The EM algorith operates by iteratively optiising an auxiliary function. In the case of H-PMHT, this function consists of a target state evolution ter, a ixing ter dependent on the target SNRs, and a easureent ter that couples the target states with the intensity ap. This easureent ter is the logarith of the easureent likelihood weighted by data association probabilities, i.e. the logarith of equation (5) with pixel-dependent scaling ters. When the sensor psf h(x t ) can be approxiated as a Gaussian then the logarith Figure 2. Point spread function h θ (θ) vs. bearing for transissions at broadside, near aft and aft of the array. of equation (5) is a su of quadratics and this can be factorised into a single quadratic, equivalent to the log-likelihood of a point-easureent [7]. Thus H-PMHT can be ipleented as an iterated data association step and pointeasureent estiation step. It is iportant to ephasise that this is not an approxiation. In this paper, the axiisation step of the H-PMHT is perfored using an extended Kalan Filter (EKF). However, the linearisation point for the EKF is odified with each EM iteration so the result is siilar to the Iterated EKF, which is known to provide a ore accurate estiate than the standard EKF [3]. Next, we will describe how the standard easureent odel for the H-PMHT algorith can be odified to include a bearing-dependent psf to odel the variation in the bea patterns for an active towed array sonar. Due to left-right abiguity issues characteristic of linear array systes, when a target is detected by a towed array, it will appear as two identical targets syetrically placed on either side of the towed array in the sensor iage. An ownship anoeuvre is required to identify a real target fro the abiguous one. Figure 1 shows representative bea patterns and the effect of left-right abiguity issues for an active towed array sonar syste at the following receive directions: Broadside: defined as 90 degrees fro the heading of the array. The bea pattern consists of a narrow bea and the two peaks generated by left-right abiguity are well-separated, Near Aft of the array: where the beas are wider and the left-right abiguous peaks begin to overlap, and Aft of the array: defined as close to 180 degrees fro the heading of the array, where the left-right bea patterns erge into a single wide peak. It can be seen that as the receive direction oves fro broadside to aft of the array, the spread in the bea pattern increases and the abiguous target in the iage erges with the real target to for a single target seared across ultiple bearing bins in the iage sensor. The half-height beawidth for the bea pattern is approxiately 8 degrees at broadside, 50 degrees (across both peaks) in the near aft direction and 42 degrees at aft. Australian Acoustical Society 3

4 17-20 Noveber 2013, Victor Harbor, Australia Figure 3. TkBD easureent iage for a target SNR return value of 24 db. In this paper, the variation in the bea pattern with receive direction will be odelled by assuing a bearing-dependent psf. Recall that a sensor's psf can be used to describe the appearance of the target in the sensor iage. For the sonar proble, the sensor outputs a easureent in range r and bearing θ space such that h( x t ) = h( r, θ ) = h r ( r) hθ ( θ ) where h r (r) and h θ (θ) are defined as the psfs for range and bearing space respectively, and assued to be independent of each other. Both psfs can be approxiated using Gaussians. For an active towed array sonar syste, the psf function h r (r) can be assued to be consistent across all bearings, however the psf in the bearing space h θ (θ will be dependent on the receive direction due to the variation of bea patterns with bearing. In this paper, a bearing-dependent psf using a Gaussian approxiation will be assued. For a given receive direction, the Gaussian psf can be calculated by setting the half-height width of the Gaussian pdf to be equal to the half-height beawidth of the current receive direction. The corresponding variance for the Gaussian psf can then be easily calculated. Figure 2 shows the resulting psfs corresponding to broadside, near aft and aft receive directions. Note that for the near aft direction, a su of two Gaussians, one for each of the left-right beas is used to odel the bea pattern. In addition, the iages used have been truncated such that when the left-right beas are well separated, only the correct bea is used. Tracks are initiated based on a peak detection thresholding process at a given SNR level and the well known M/N logic [5] is iposed to upgrade fro tentative to confired status. The transition atrix for the target dynaics is given by a constant velocity odel which varies depending on the tie between consecutive transissions. (6) 3 COMPARATIVE STUDY USING SONAR DATA In this section, the perforance of the H-PMHT is copared with that of IPDA using archived sonar data. Both the H- PMHT and IPDA perforance is quantified for a set of SNR Figure 4. TkBD easureent iage for a target SNR return value of 13 db. thresholds. For the IPDA, the SNR threshold will deterine the nuber of detections that are passed to the tracker. In the case of the H-PMHT, the SNR threshold will be used in a peak detector for track initiation. The data used in this paper originates fro a series of sonar trials conducted by the Defence Science and Technology Organisation (DSTO) fro May to August 2003 using a containerised active towed array deonstration sonar syste called CASSTASS. The sonar trials featured a line array towed behind a oving surface ship at two different locations in the Western Australian exercise Area (WAXA). The two datasets feature characteristics that are unique to the sonar detection and tracking proble in a shallow environent with water depths fro and for an interediate ocean environent with depths fro Transissions were set to detect possible targets with a axiu range of 60 k with the ajority of transissions being in the aft direction. The datasets feature a fluctuating target and persistent clutter detections that are the result of reflections fro bathyetric features along the continental shelf. Both datasets consist of approxiately 20 transissions with the tie duration between transissions being approxiately 90 seconds. The target is an echo-repeater (ER) ade to siulate the returns fro a siple point-like target in the ocean environent. During the trial, the ER platfor was observed to have an average travelling speed of 0-4 knots with varying target strengths of 9, 19 and 29 db. The SNR for the two datasets is approxiately 29 db, which is relatively high, and it is expected that both the IPDA and TkBD will be able to for on the ER. However, variations in perforance are also expected as the SNR for the ER did fluctuate with tie, with SNR levels as low as 13 db being observed. Both the IPDA and H-PMHT tracked using global Cartesian coordinates with an origin fixed at the last recorded ownship position in each trial. The IPDA algorith used point-easureent detections which were generated fro an autoated detection schee featuring clustering. To gain an idea of the sensitivity of conventional tracking to thresholding, the IPDA algorith was ipleented using three detection thresholding levels at 11, 13 and 15 db. The expected nuber of clutter easureents was odelled using a Poisson distribution with paraeter λ= N k / V k where V k denotes the area of surveillance and N k was 4 Australian Acoustical Society

5 17-20 Noveber 2013, Victor Harbor, Australia estiated using the average nuber of point detections which varied with the SNR thresholding level. The IPDA algorith initiated tentative using two-point differencing. When the probability of existence for a track rose above 0.5, tentative tacks were upgraded to confired status. Tracks were terinated when the probability existence fell below a threshold of 0.3. For the TkBD case, the agnitude of the sensor returns in ters of power was collected in bearing and range cells consisting of 181 bea bins at 2 degree intervals fro 0 to 360 degrees and approxiately a few hundred range bins, with range intervals of approxiately 60. Figure 3 and Figure 4 show exaples of TkBD easureent iages across range and bearing space for target SNR values of 24 db and 13 db respectively. The true target position is indicated by the red circle. Clearly, when the target SNR is high, the target return is easily distinguishable fro the background clutter. However when the target SNR drops, it is ore difficult to detect the target fro the background clutter. It is also iportant to realise that as the resolution of the bearing bins is finer than the beawidth of the sensor, it is expected that the target returns will be spread over ultiple bearing bins. For track initiation, the H-PMHT algorith applied a peak detection threshold to the sensor iage according to a certain SNR threshold and then used two-point differencing to initiate tentative. In the case when the current position estiates of several tentative were within 250 in position, the highest SNR track was retained and all other were discarded. A easure for the track quality was derived using target SNR calculated fro the ixing proportions estiates. Tracks were confired and terinated using a 3/5 logic rule requiring this track quality easure to be above a threshold for 3 out of 5 returns. Multi-target ipleentations were used to copare TkBD to conventional tracking. In both algoriths, it was assued that background noise was unifor and easureent noise followed a Gaussian distribution. Due to the high volue of data, a tie-recursive H-PMHT filter was used in the analysis rather than processing the sequence as a batch. For the H- PMHT, a axiu of ten EM iterations were perfored at each tie scan. 4 RESULTS The tracking outputs of the H-PMHT and the IPDA algorith for the two sets of trials data is now presented. The fro the two algoriths were copared with truth data provided by GPS logs. Figures 5, 6 and 7 show the tracking results in both datasets at SNR thresholding levels of 11, 13 and 15 db respectively. In these figures, the IPDA algorith used detections thresholded at the respective SNR level while the H-PMHT algorith used the sae SNR level to initiate using a peak detection thresholding schee. It is iportant to realise that although the H-PMHT initiated on thresholded peaks, state estiates were updated using the entire raw iage data. For the interediate dataset, anual detections which have been visually picked out with the naked eye by a sonar operator are shown in green. Observe that there is a bias between the ground truth given by the GPS logs shown in black and the anual detections shown in green in the interediate dataset. The differences are due to effects of current on the towed array, which have not been taken into account. Tables 1 and 2 show the average nuber of easureents at each tie frae received by the IPDA at each thresholding level for the shallow and interediate dataset respectively. The tables also collate the nuber of false and divergent fored by the IPDA in each dataset. A track is considered divergent if it successfully initiated a track on the target, but was seduced away due to spurious easureents. Table 1. Nuber of false and divergent IPDA at different SNR thresholding levels for the shallow dataset. Threshold Level (db) Average nuber of detections per frae Nuber of divergent Nuber of false Table 2. Nuber of false and divergent IPDA at different SNR thresholding levels for the interediate dataset. Threshold Level (db) Average nuber of detections per frae Nuber of divergent Nuber of false The H-PMHT algorith was able to track the ER target with zero false and divergent fored in all scenarios. It can be seen that at SNR thresholding level of 11 db, on average the IPDA processed over 100 detections at each tie frae. The IPDA algorith was unable to for sensible because of the large nuber of detections, which served to increase the size of the covariance and hence the validation gate at each iteration. As a result, the IPDA was unable to for a track on the ER target in the shallow dataset and although it did for one target track in the interediate dataset, the track rapidly diverged after several tie scans. Figure 5(a) only displays fro the H-PMHT algorith as the IPDA algorith produced 8 spurious false which were not related to the ER target. For siilar reasons, Figure 5(b) only shows the track fro the H-PMHT algorith and the single divergent track fro IPDA, and none of the false IPDA. At a SNR thresholding level of 13 db, the IPDA algorith fored a track on the ER target in the shallow dataset but was only able to for a divergent track in the interediate dataset. When the SNR threshold level was raised to 15 db, the IPDA was able to for a track on the ER target in both datasets with zero false and divergent. The likelihood of initiating and aintaining a track on a low SNR target at higher thresholds would be negligible as no detections would be obtained. Even if the SNR threshold was lowered, it would still be difficult to for a track on a low SNR target due to the sheer nuber of detections as observed at the low SNR thresholds here. 5 SUMMARY This paper presents a coparison of the tracking perforance of a TkBD algorith using H-PMHT with the outputs of a conventional IPDA tracker with ulti-target logic using point detections. The algoriths were tested on archived data fro Australian Acoustical Society 5

6 17-20 Noveber 2013, Victor Harbor, Australia (a) Shallow (b) Interediate Figure 5. Tracking Results for H-PMHT vs. IPDA using a SNR thresholding level at 11 db. (a) Shallow (b) Interediate Figure 6. Tracking Results for H-PMHT vs. IPDA using a SNR thresholding level at 13 db. (a) Shallow (b) Interediate Figure 7. Tracking Results for H-PMHT vs. IPDA using a SNR thresholding level at 15 db. 6 Australian Acoustical Society

7 17-20 Noveber 2013, Victor Harbor, Australia an active towed array sonar syste collected off the coast of Western Australia. This paper has deonstrated that for ulti- target tracking in shallow and interediate scenarios, TkBD can provide significant perforance advantages over the IPDA ipleentation. The test data contained a target which gave relatively high SNR returns on ost scans so the IPDA was able to for a reliable track when a high SNR threshold was applied during the point-easureent extraction stage. In contrast the H-PMHT processed the intensity ap data directly without an explicit SNR threshold (except artificially iposed for track initiation) and was able to detect the target without foring any false. In future work, we will consider testing the algoriths on datasets featuring low SNR targets. An extension of the TkBD algorith to include a ulti-path target odel to aid in the detection of targets in deep water scenarios will also be considered. Musicki, D, Wang, X, Elle, R & Fletcher, F 2007, Efficient Active Sonar Multitarget Tracking, OCEANS 2006, pp.1-8. Orlando, D, Ehlers, F & Ricci, G 2010, Track-before-detect Algoriths for Bistatic Sonars, International Workshop on Cognitive Inforation Processing, pp Streit, RL 2000, Tracking on intensity-odulated data streas, Technical report 11221, NUWC, RI, USA. Streit, RL & Luginbuhl, TE 1995, Probabilistic ultihypothesis tracking, Technical report 10428, NUWC, RI, USA. Tonissen, SM & Evans, RJ 1996, Perforance of dynaic prograing techniques for Track-Before-Detect, IEEE Transactions on Aerospace and Electronic Systes, vol 32, no. 4, pp REFERENCES Aughenbaugh, JM & La Cour, BR 2009, Use of Prior Inforation in Active Sonar Tracking, Proceedings of the 12th International Conference on Inforation Fusion. Babu, VS, Shankar, MR, Majudar, S & Rao, SK 2001, IMM Unscented Kalan Filter Based Tracking of Maneuvering Targets using Active Sonar Measureents, 2011 International Conference on Counications and Signal Processing (ICCSP), pp Bar-Shalo, Y, Li, XR & Kirubarajan, TE 2001, Estiation with Applications to Tracking and Navigation Theory, Algorith and Software, Wiley, New York. Blanding, WR, Willett, PK, Bar-Shalo, Y & Coraluppi, S 2009, Multisensor Track Manageent for Targets with Fluctuating SNR, IEEE Transactions on Aerospace and Electronic Syste, vol. 45, no.4, pp Castella, FR 1976, Sliding Window Detection Probabilities, IEEE Transactions on Aerospace and Electronic Systes, vol. 12, pp Colegrove, SB, Davis, AW & Ayliffe, JK 1986, Track Initiation and Nearest Neighbours Incorporated into Probabilistic Data Association, Journal of Electrical and Electronics Engineering, Australia, vol. 6, no, 3, pp Davey, SJ 2011, Histogra PMHT with Particles, Proceedings of the 14th International Conference on Inforation Fusion, Chicago, USA. Davey, SJ, Rutten, MG & Cheung, B 2008, A coparison of detection perforance for several track-before-detect Algoriths, EURASIP Journal on Advances in Signal Processing. El-Jaber, M, Osan, A, Mellea,G & Nourledin, A 2009, Target Tracking in Multi-Static Active Sonar Systes using Dynaic Prograing and Hough Transfor, Proceedings of the 14th International Conference on Inforation Fusion, Chicago, USA. Hepel, CG & Doran, SL 2004, A PMHT algorith for active sonar, Proceedings of SPIE 5430, Acquisition, Tracking, and Pointing XVIII, 132. Luginbuhl, TE & Willett, P 2004, Estiating the Paraeters of General Frequency Modulated Signals, IEEE Transactions on Signal Processing, vol. 52, no. 1, pp Musicki, D, Evans, R & Stankovic, S 1994, Integrated Proabilistic Data Association', IEEE Transactions on Autoatic Control, vol. 39, no. 6, pp Musicki, D & Evans, R 2004, Joint Integrated Probabilistic Data Association: JIPDA, IEEE Transactions on Aerospace and Electronic Systes, vol. 40, no. 3, pp Australian Acoustical Society 7